. . "In mathematics, the Fortuin\u2013Kasteleyn\u2013Ginibre (FKG) inequality is a correlation inequality, a fundamental tool in statistical mechanics and probabilistic combinatorics (especially random graphs and the probabilistic method), due to , Pieter W. Kasteleyn, and Jean Ginibre. Informally, it says that in many random systems, increasing events are positively correlated, while an increasing and a decreasing event are negatively correlated. It was obtained by studying the random cluster model. An earlier version, for the special case of i.i.d. variables, called Harris inequality, is due to Theodore Edward Harris, see . One generalization of the FKG inequality is the below, and an even further generalization is the Ahlswede\u2013Daykin \"four functions\" theorem (1978). Furthermore, it has the same conclusion as the Griffiths inequalities, but the hypotheses are different."@en . "89"^^ . . . . . "In\u00E9galit\u00E9 FKG"@fr . . "Jean"@en . . . . "Cees M."@en . . . . . . . . . . . . . . . . "20283423"^^ . "Correlation inequalities on some partially ordered sets"@en . "Pieter W."@en . "1123340233"^^ . . . . "Kasteleyn"@en . "In mathematics, the Fortuin\u2013Kasteleyn\u2013Ginibre (FKG) inequality is a correlation inequality, a fundamental tool in statistical mechanics and probabilistic combinatorics (especially random graphs and the probabilistic method), due to , Pieter W. Kasteleyn, and Jean Ginibre. Informally, it says that in many random systems, increasing events are positively correlated, while an increasing and a decreasing event are negatively correlated. It was obtained by studying the random cluster model."@en . . . "Fortuin"@en . . . "Pieter Kasteleyn"@en . "FKG inequality"@en . . . "L\u2019in\u00E9galit\u00E9 FKG, notion due \u00E0 Fortuin, Kasteleyn et Ginibreest une version g\u00E9n\u00E9ralis\u00E9e de l'in\u00E9galit\u00E9 de Tchebychev pour les sommes. C'est une in\u00E9galit\u00E9 de corr\u00E9lation utilis\u00E9e, par exemple, en th\u00E9orie de la percolation, et dans l'\u00E9tude du mod\u00E8le de graphes al\u00E9atoires d\u00FB \u00E0 Paul Erd\u0151s et Alfr\u00E9d R\u00E9nyi : le (en)."@fr . . . . "Cees M. Fortuin"@en . "Fishburn"@en . "1971"^^ . . . "Jean Ginibre"@en . "Communications in Mathematical Physics"@en . . . . . "P.C."@en . . . . . . . "15747"^^ . . . . "L\u2019in\u00E9galit\u00E9 FKG, notion due \u00E0 Fortuin, Kasteleyn et Ginibreest une version g\u00E9n\u00E9ralis\u00E9e de l'in\u00E9galit\u00E9 de Tchebychev pour les sommes. C'est une in\u00E9galit\u00E9 de corr\u00E9lation utilis\u00E9e, par exemple, en th\u00E9orie de la percolation, et dans l'\u00E9tude du mod\u00E8le de graphes al\u00E9atoires d\u00FB \u00E0 Paul Erd\u0151s et Alfr\u00E9d R\u00E9nyi : le (en)."@fr . . . . . . "FKG inequality"@en . . . . "309498"^^ . . . "Ginibre"@en . "22"^^ . . .